C4 Mathematics Edexcel June 2010 Question 1

Figure 1 shows part of the curve with equation y = √(0.75 + cos2x)
The finite region R, shown shaded in Figure 1, is bounded by the curve, the y-axis, the x-axis and the line with
equation x = π/3
(a) Complete the table with values of y corresponding to x = π/6 and x = π/4

(b) Use the trapezium rule
(i) with the values of y at x = 0, x = π/6 and x = π/3 to find an estimate of the area of R. Give your answer to 3 decimal places.
(ii) with the values of y at x = 0, x = π/12, x = π/6, x = π/4 and x = π/3 to find a further estimate of the area of R. Give your answer to 3 decimal places.